CN114859732A - Feedforward compensation active disturbance rejection controller based on scheduling signal and design method thereof - Google Patents

Feedforward compensation active disturbance rejection controller based on scheduling signal and design method thereof Download PDF

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CN114859732A
CN114859732A CN202210551315.XA CN202210551315A CN114859732A CN 114859732 A CN114859732 A CN 114859732A CN 202210551315 A CN202210551315 A CN 202210551315A CN 114859732 A CN114859732 A CN 114859732A
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薛亚丽
王佑
李政
叶青
颜纲要
张业才
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Guoneng Bengbu Power Generation Co ltd
Tsinghua University
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Tsinghua University
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Abstract

The invention discloses a feedforward compensation active disturbance rejection controller based on a scheduling signal and a design method thereof, and aims to solve the problem of poor control quality when a large-inertia process runs under large-range frequent variable working conditions. The active disturbance rejection controller comprises a feedforward controller, a feedback controller, a compensation module and an extended state observer. By introducing a scheduling signal, variable parameter design and real-time adjustment are respectively carried out on the feedforward controller, the feedback controller, the compensation module and the extended state observer, and dynamic model information of a controlled process under a variable working condition is utilized in the process, so that the adaptability of the active disturbance rejection controller to large inertia and the variable working condition can be improved. The control system has simple structure, simple setting method and good engineering application prospect.

Description

Feedforward compensation active disturbance rejection controller based on scheduling signal and design method thereof
Technical Field
The invention relates to the technical field of industrial automation, in particular to a feedforward compensation active disturbance rejection controller based on a scheduling signal and a design method thereof.
Background
Active Disturbance Rejection Control (ADRC) is an advanced Control method that combines classical PID Control with modern Control theory. The earliest ADRCs were nonlinear controllers consisting of a tracking differentiator, a nonlinear combination and an extended state observer. However, the nonlinear ADRC has a complex structure and is difficult to adjust the parameters of the controller, so that the linear ADRC is generally applied. The basic structure of Linear ADRC includes two parts, Error-based Linear Function (ELF) and Extended State Observer (ESO). Compared with other advanced control algorithms, the linear ADRC does not depend on an accurate model of a controlled object, has the advantages of simple structure, convenience in setting, good anti-interference performance and strong robustness, and is applied and developed in the field of industrial process control in recent years.
However, when linear ADRC is applied to automatic control of a large thermodynamic process, two problems are mainly faced, namely, when the inertia and the lag of the controlled process are large, the observation effect of ESO is poor, and the control effect of ADRC is not ideal; and secondly, when the working condition of the controlled process changes frequently in a large range, the ADRC control performance designed according to the rated working condition becomes poor. Patent document CN107703746A proposes that the ability to track when the set value changes rapidly can be improved by using a linear combination of the derivatives of the respective orders of the set value as the feedforward control amount of the ADRC. The design of a linear active disturbance rejection controller of a high-order large-inertia system (control and decision, 3 months 2022) of king you et al provides an ADRC control structure and a parameter setting method for compensation by using model information, and improves the control effect of the ADRC on the large-inertia process. However, the control effect of the method is limited to solve the problem of the thermodynamic process control, namely, when the inertia of the controlled process is large and the dynamic characteristic changes obviously with the working condition.
Disclosure of Invention
The invention provides a feedforward compensation active disturbance rejection controller based on a scheduling signal and a design method thereof, aiming at solving the problem of poor control quality of a large-inertia process when the large-inertia process runs under a large-range frequent variable working condition.
The invention is realized by the following technical scheme.
In one aspect of the invention, a feedforward compensation active disturbance rejection controller based on a scheduling signal is provided and comprises a feedforward controller, a feedback controller, a compensation module and an extended state observer.
The feedforward controller is as follows: u. of Q (t) ═ F1(q (t)), where u Q (t) is a feedforward control quantity, Q (t) is a scheduling signal, and F1(·) is a feedforward function.
The feedback controller is as follows:
Figure BDA0003650866280000021
wherein u is C (t) is the output of the feedback controller, r (t) is a set value, z i (t) (i ═ 1,2, …, m +1) is the output of the extended state observer,
Figure BDA0003650866280000022
and b 0 (t) is a tunable parameter and varies with the variation of the modulation signal Q (t).
Output u of the feedback controller C (t) can be an input to the compensation module.
The compensation module is as follows: u. of TF (t)＝F2(u C (t),T F2 (t, p) wherein u TF (T) is the output of the compensation module, F2 (-) is the compensation function, T F2 (T) and p are adjustable parameters, T F2 (t) varies with the change in the scheduling signal Q (t).
Output u of the compensation module TF (t) can be an input to the extended state observer.
The feedback controlThe output of the controller and the output of the feedforward controller form the control law of the active disturbance rejection controller, and the control law comprises the following steps: u (t) ═ u Q (t)+u C (t), wherein u (t) is a control amount.
In the above technical solution, the extended state observer is:
Figure BDA0003650866280000023
wherein y (t) is a controlled quantity, beta i (t) (i ═ 1,2, …, m +1) is a variable parameter of the extended state observer, varying as a function of the modulation signal q (t), b 0 (t) is an adjustable parameter of the feedback controller.
In the above technical solution, a transfer function of the compensation function (i.e. a frequency domain form of the compensation function) is:
Figure BDA0003650866280000024
wherein F2(s) is the transfer function of the compensation function, U TF (s) and U C (s) the output u of the compensation module and the feedback controller, respectively TF (t) and u C (T) pull transform, p is the transfer function order of the compensation function, T F2 (T) and p are both adjustable parameters, and T is F2 (t) varies in value as the modulation signal Q (t) varies.
Another aspect of the present invention provides a method for designing a feedforward compensation active disturbance rejection controller based on a scheduling signal, including the steps of:
s1, selecting a scheduling signal Q (t) according to the variable working condition characteristics of the controlled process, and obtaining the functional relation between the scheduling signal Q (t) and the feedforward control quantity according to design calculation or field experiments;
s2, obtaining a feedforward function F1 (-) according to a function relation inverse function of the scheduling signal Q (t) and the feedforward control quantity; calculating to obtain feedforward control quantity u according to feedforward function and scheduling signal Q (t)＝F1(Q(t))；
S3, acquiring dynamic information of the variable working condition of the controlled process;
s4, designing a compensation module and a compensation function F2 (-) thereof, and obtaining the output u of the compensation module by using the variable working condition dynamic information obtained in S3 TF (t)＝F2(u C (t),T F2 (t), p), wherein F2(·) is a compensation function, u C (T) is the output of the feedback controller, T F2 (t) and p are adjustable parameters;
designing an extended state observer, wherein the output of the compensation module can be used as the input of the extended state observer to obtain the output z of the extended state observer i (t)(i＝1,2,…,m+1)；
S6, designing a feedback controller, and calculating to obtain a feedback control quantity u C (t)：
Figure BDA0003650866280000031
Wherein r (t) is a set value,
Figure BDA0003650866280000032
Figure BDA0003650866280000033
and b 0 (t) is an adjustable parameter;
and S7, forming a control law of the active disturbance rejection controller, and obtaining a control quantity of the active disturbance rejection controller through the feedforward control quantity and the feedback control quantity:
u(t)＝u Q (t)+u C (t)。
in the above technical solution, the selection of the scheduling signal q (t) simultaneously satisfies the following two conditions:
(1) the variable working condition characteristics of the controlled process can be represented;
(2) has a programmable functional relationship with the amount of feedforward control.
According to one embodiment, the method for acquiring the dynamic information of the variable operating conditions of the controlled process in step S3 includes:
dividing the variable working condition range of the controlled process into q sections according to the nonlinearity of the controlled process, obtaining the dynamic information of each section and expressing the dynamic information as follows through a controlled process transfer function (high-order linear function):
Figure BDA0003650866280000034
where s is laplace operator, y(s) and u(s) are laplace transforms of y (t) and u (t), respectively, the subscript γ 2(γ 2 ═ 1,2, …, q) is the operating condition number, G is the operating condition number, and G is the operating condition number p,γ2 (s) is the transfer function of the controlled process under the working condition gamma 2, K γ2 System gain, T, for operating condition gamma 2 γ2 And n is the order of the transfer function of the controlled process, which is the time constant under the working condition gamma 2.
In the above technical solution, the transfer function of the compensation function is designed as follows:
Figure BDA0003650866280000035
wherein F2(s) is a transfer function of the compensation function F2 (-), U TF (s) and U C (s) are each u TF (t) and u C (T) pull-type transformation, T F2 (t) and p are adjustable parameters.
In the above technical solution, the adjustable parameter T F2 (t) is designed as follows:
T F2 (t)＝ γ (t)＝F Tγ (Q(t),{Q r2 },{T γ2 })，(γ2＝1,2,…,q)，
wherein, { T γ2 The time constant of each working condition in the variable working condition dynamic information is { Q } r2 The scheduling signal value under each working condition, Q (t) is a scheduling signal, F Tγ (. cndot.) is a linear or non-linear function; t is γ And (t) is the output of the function, and represents the corresponding time constant of the scheduling signal Q (t).
In the above technical solution, the adjustable parameter p of the compensation function is designed as follows: p-n-m. Where n is the order of the transfer function of the process being controlled and m is the order of the feedback controller.
In the above technical solution, the output u of the compensation module TF The time domain form of (t) is:
Figure BDA0003650866280000041
where Δ T is the calculation period and k is the discrete time sequence.
In the above technical solution, the extended state observer is designed as follows:
Figure BDA0003650866280000042
wherein y (t) is a controlled quantity, beta i (t) (i ═ 1,2, …, m +1) is a variable parameter of the extended state observer, varying as a function of the modulation signal q (t), b 0 (t) is an adjustable parameter of the feedback controller.
In the above technical solution, the adjustable parameter β of the extended state observer is i (t) (i ═ 1,2, …, m +1) can be chosen as follows:
Figure BDA0003650866280000043
wherein, ω is o (t) is the state observer bandwidth,
Figure BDA0003650866280000044
wherein, T γ (t) is the time constant corresponding to the scheduling signal q (t).
In the above technical solution, the adjustable parameter of the feedback controller
Figure BDA0003650866280000045
The design is as follows:
Figure BDA0003650866280000046
where m is the order of the feedback controller, ω c (T) is the feedback controller bandwidth, T γ (t) varies with the scheduling signal Q (t).
In the above technical solution, the adjustable parameter b of the feedback controller 0 (t) is designed as:
Figure BDA0003650866280000047
wherein, T γ (t) and K γ (t) are all varied with the scheduling signal Q (t).
Wherein, K γ (t) is calculated as:
K γ (t)＝F Kγ (Q(t),{Q r2 },{K γ2 }，
wherein { K γ2 The time constant under each working condition in the dynamic information of the controlled process variable working condition, { Q } r2 The scheduling signal value under each working condition, Q (t) is a scheduling signal, F Kγ (. cndot.) is a linear or non-linear function; k γ (t) is the output of the function, characterizing the system gain corresponding to the scheduling signal Q (t).
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention provides a feedforward compensation active disturbance rejection controller based on a scheduling signal and a design method thereof aiming at a large inertia controlled process of frequent variable working conditions. The control system has simple structure, simple setting method and good engineering application prospect.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
Fig. 1 is a schematic structural diagram of a feedforward compensated active disturbance rejection controller based on a scheduling signal according to an embodiment of the present invention.
Fig. 2 is a comparison diagram of the rated operating condition controlled quantity curve provided in embodiment 1 of the present invention.
Fig. 3 is a schematic diagram comparing the control quantity curve of the rated operating condition provided in embodiment 1 of the present invention.
Fig. 4 is a comparison diagram of the variable condition controlled quantity curve provided in embodiment 1 of the present invention.
Fig. 5 is a comparison diagram of the variable operation condition controlled variable curve provided in embodiment 1 of the present invention.
Fig. 6 is a comparison diagram of controlled quantity curves under lifting load according to embodiment 2 of the present invention.
Fig. 7 is a schematic diagram comparing curves of control amounts under the lifting load according to embodiment 2 of the present invention.
In the figure:
r (t) is a set value, y (t) is a controlled quantity, u c (t) is a feedback control amount, u Q (t) is a feedforward control quantity, u (t) is a control quantity TF (t) is the output of the compensation module, z 1 (t)～z m+1 (t) is the output of the extended state observer, and Q (t) is the scheduling signal.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Furthermore, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. In the description of the following examples, "plurality" means two or more unless specifically limited otherwise.
The invention provides a feedforward compensation active disturbance rejection controller based on a scheduling signal, which is suitable for active disturbance rejection control of a controlled process (or a controlled object). The control system (system for short) of the invention comprises the active disturbance rejection controller and the applied controlled process thereof. As shown in fig. 1, in order to solve the problem of poor control quality when a large inertia process operates under a large-scale frequent variable working condition, in the design of the active disturbance rejection controller, the invention introduces a scheduling signal and utilizes dynamic model information of a controlled process under the variable working condition to respectively carry out variable parameter design and real-time adjustment on the feedforward controller, the feedback controller, the compensation module and the extended state observer, thereby improving the adaptability of the active disturbance rejection controller to the large inertia and the variable working condition.
The control law of the active disturbance rejection controller constructed by the invention is that the control quantity of the active disturbance rejection controller is obtained through the feedforward control quantity and the feedback control quantity: u (t) ═ u Q (t)+u C (t)。
S1, selecting a scheduling signal
And selecting a scheduling signal Q (t) according to the variable working condition characteristics of the controlled process, and obtaining the functional relation between the scheduling signal Q (t) and the feedforward control quantity according to design calculation or field experiments.
The scheduling signal q (t) can be selected according to the physical working mechanism of the controlled process, and the following two conditions need to be satisfied simultaneously:
(1) the variable working condition characteristic of the controlled process can be represented, namely the expected working condition of the controlled process in the variable load process can be represented. Such as a power generation load command of the thermal power generating unit.
(2) The function relation with the feedforward control quantity can be designed, for example, when the power generation load instruction of the thermal power generating unit is used as a dispatching signal, and the basic coal feeding quantity is used as a preset feedforward control quantity, the function relation between the power generation load instruction and the basic coal feeding quantity can be obtained in advance through design calculation or field experiments.
S2 design feedforward function and feedforward controller
The feedforward function F1(·) may be a linear function or a nonlinear function, and is designed according to a physical relationship between the feedforward control amount and the scheduling signal. The feedforward controller has the effect that when the scheduling signal changes, so that the expected working condition of the controlled process changes, the control quantity can change rapidly according to the change of the scheduling signal Q (t), and the response process of the control system is accelerated.
The feedforward controller comprises the following feedforward control quantity: u. of Q (t)＝F1(Q(t))。
The feedforward function F1 (-) can be obtained by inverting the function of the scheduling signal q (t) as a function of the feedforward control quantity.
According to the above step S1, the functional relationship between the feedforward control amount and the scheduling signal in the variable condition range can be obtained by design calculation or field experiment, i.e. the feedforward function F1(·) can be determined by a negation function. For example, if q (t) ═ F1 is obtained from a steady-state experiment f (u (t)), a feedforward function F1 () can be designed and derived
Figure BDA0003650866280000061
Figure BDA0003650866280000074
Obtaining a feedforward control quantity (output of a feedforward controller), wherein Q (t) is a scheduling signal, k f Is an adjustable parameter representing the strength of the feed-forward action.
S3, obtaining the dynamic information of the controlled process
Dividing the variable working condition range into q sections according to the nonlinearity of the controlled process, wherein the dynamic information of each section is represented by a linear high-order transfer function, namely the transfer function of the controlled process is as follows:
Figure BDA0003650866280000071
where s is laplace operator, y(s) and u(s) are laplace transforms of y (t) and u (t), respectively, the subscript γ 2(γ 2 ═ 1,2, …, q) is the operating condition number, F is the operating condition number p,γ2 (s) is the transfer function of the controlled process under the working condition gamma 2, K γ2 System gain, T, for operating condition gamma 2 γ2 Is the time constant under the working condition gamma 2And n is the order of the transfer function of the controlled process.
S4 design of compensation module and compensation function
The compensation module and the compensation function have the effects that when the working condition of the system changes so that the dispatching signal changes, a dynamic compensation effect matched with the dynamic characteristic of the controlled process is generated and sent to the extended state observer, the state observation error is reduced, and the control effect of the controller on the large-inertia process is improved.
The design of the compensation function F2 (-) can be represented in frequency domain or time domain based on the acquired dynamic information of the variation condition of the controlled process.
The frequency domain form of the compensation function, i.e. the transfer function, is:
Figure BDA0003650866280000072
where F2(s) is the transfer function of the compensation function, U TF (s) and U C (s) is each u TF (t) and u C (T) pull transformation, T F2 (t) and p are adjustable parameters.
Output u of compensation module TF The time domain form of (t) is:
Figure BDA0003650866280000073
where Δ T is the calculation period and k is the discrete time sequence.
Adjustable parameter in the compensation function as T F2 (t) and p. In the invention, the selection method comprises the following steps:
T F2 the value of (T) changes with the dispatching signal Q (T) in order to match the change rule of the dynamic characteristic of the controlled process with the working condition, thereby reducing the order of the equivalent observed object of the extended state observer and improving the state observation effect, therefore T F2 And (t) determining the real-time value according to the variable working condition dynamic information of the controlled process and the scheduling signal, namely:
T F2 (t)＝T γ (t)＝F Tγ (Q(t),{Q r2 },{T γ2 })，(γ2＝1,2,…,q)
wherein, { T γ2 The time constant of each working condition in the variable working condition dynamic information is { Q } r2 The scheduling signal value under each working condition, Q (t) is a scheduling signal, F Tγ (. cndot.) is a linear or non-linear function, T γ And (t) is the output of the function, and represents the corresponding time constant of the scheduling signal Q (t).
The choice of the adjustable parameter p depends on the order of the active disturbance rejection controller employed. If the order of the controlled process is n and the order of the active disturbance rejection controller is m, the order of the extended state observer is m +1, and the order p of the compensation module is: p-n-m. This selection enables the states not included in the compensation module to be observed in their entirety by the extended state observer.
S5, designing an extended state observer
The time domain form of the extended state observer is as follows:
Figure BDA0003650866280000081
β i (t) (i ═ 1,2, … m +1) are adjustable parameters of the extended state observer, and b0(t) are adjustable parameters of the feedback controller, and all the parameters are changed along with the adjusting signal q (t).
In a programmable control system, an Euler method is used for discretizing an extended state observer, and the expression is as follows:
Figure BDA0003650866280000082
where Δ T represents a calculation period and k represents a discrete time sequence.
Adjustable parameter beta of extended state observer i (t) (i ═ 1,2, …, m +1) was chosen as follows:
Figure BDA0003650866280000083
wherein, ω is o (t) is the extended state observer bandwidth,
Figure BDA0003650866280000084
wherein, T γ (t) is the time constant corresponding to the scheduling signal q (t).
S6, designing a feedback controller
The feedback control quantity is calculated by the feedback controller according to the set value and the output of the extended state observer to obtain:
Figure BDA0003650866280000085
wherein u is C (t) is a feedback control amount, r (t) is a set value of a control system, and z i (t) (i ═ 1,2, …, m +1) is the output of the extended state observer,
Figure BDA0003650866280000091
and b 0 And (t) is an adjustable parameter of the feedback controller, and is changed along with the adjusting signal Q (t). Wherein
Figure BDA0003650866280000092
Can be parameterized according to the bandwidth and is based on the bandwidth omega of the controller c (t) can be calculated and can also be determined by an optimization algorithm or field tests. b 0 (t) is an estimate of the higher order gain of the controlled process, as a function of the scheduling signal Q (t). The feedback controller has the function that when the working condition changes or disturbance occurs, the feedback controller can adjust the controlled quantity according to the set value and the output of the extended state observer, counteract the observed total disturbance and finally eliminate the control deviation.
Adjustable parameters of the feedback controller
Figure BDA0003650866280000093
The design is as follows:
Figure BDA0003650866280000094
where m is the order of the feedback controller, ω c (T) is the feedback controller bandwidth, T γ (t) varies with the scheduling signal Q (t).
Adjustable parameter b of the feedback controller 0 (t) is designed as:
Figure BDA0003650866280000095
wherein, T γ (t) and K γ (t) are all varied with the scheduling signal Q (t).
K γ (t) is calculated as:
K γ (t)＝K Kγ (Q(t),{Q r2 },{K γ2 }
wherein { K γ2 Is the time constant under each working condition in the dynamic information of the controlled process variable working condition, { Q r2 The scheduling signal value under each working condition, Q (t) is a scheduling signal, F Kγ (. is a linear or non-linear function, K γ (t) is the output of the function, and represents the system gain corresponding to the scheduling signal Q (t).
Function F for simplicity of use Kγ (. cndot.) and F Tγ (. cndot.) can be taken as a linear interpolation function.
The control quantity of the feedforward compensation active disturbance rejection controller based on the scheduling signal is the sum of the feedforward control quantity and the feedback control quantity, namely:
u(t)＝u Q (t)+u C (t)。
the control effect of the present invention will be described below by taking two simulation examples as examples.
Example 1: under a rated working condition, the transfer function of a controlled object of the main steam pressure of a certain coal burner group is as follows:
Figure BDA0003650866280000096
the time constant T varies between 30-50 as the operating conditions change.
To illustrate the control effect of the present inventionFruit, first using the method of the present invention and taking k f The design was done at 0 and compared to conventional ADRC and ADRC with set-point feed forward of comparative example 1 (patent CN107703746A) and compensated ADRC of comparative example 2 (Wang et al, design of linear active disturbance rejection controller for high order macroinertia systems, control and decision, 3.3.3.2022, https:// doi.org/10.13195/j.kzyjc.2021.1576).
Taking the order of the feedback controller as m-2, according to the design method of the invention, the order of the extended state observer is m + 1-3, and the order of the compensation function is n-m-3. Under rated working condition, taking time constant T of compensation function F2 50, controller bandwidth of 0.02, extended state observer bandwidth of 1, control parameter of b 0 ＝1.12×10 -5 ，β 1 ＝3，β 2 ＝3，β 3 ＝1，k 1 ＝4×10 -4 ，k 2 0.04. Under a rated working condition, the traditional ADRC and the ADRC of comparative example 1 are designed, the bandwidth of a controller is 0.02, the bandwidth of an extended state observer is 0.2, and a control parameter is b 0 ＝2.0158×10 -4 ，β 1 ＝0.6，β 2 ＝0.12，β 3 ＝0.008，k 1 ＝4×10 -4 ，k 2 0.04. And simulating the control effect of the three methods.
FIG. 2 is a set point step response and disturbance response curve under a rated operating condition. The unit step change of the set value occurs at 1000 seconds, and the step disturbance with the amplitude of 0.5 occurs at 5000 seconds in the input quantity of the controlled process. It can be seen from the curves that the ADRCs with compensation of the design of the present invention are able to reach the setpoint faster and without overshoot than the conventional ADRCs and the ADRCs with setpoint feed forward of comparative example 1 at a step change of the setpoint. When the input of the controlled process is disturbed, the ADRC designed by the invention can eliminate the influence of the disturbance more quickly, and the dynamic deviation is minimum.
FIG. 3 is a control amount variation curve under a rated operating condition. It can be seen that the change of the ADRC control quantity with compensation designed by the invention is more rapid and smooth, the ADRC control quantity of the comparative example 1 has overlarge instantaneous fluctuation in the step response of the set value, and the conventional ADRC control quantity is obviously slower.
Fig. 4 is a comparison graph of the set point step response and the disturbance response when the operating condition is changed to T-30. The second order compensation ADRC of comparative example 2 is added, whose parameters are consistent with those of ADRC of the present invention under nominal conditions, but do not vary with the conditions. As the control parameter of the variable parameter ADRC with compensation is changed along with the working condition, the controlled quantity can more quickly and stably reach a new set value without overshoot; the ADRC with compensation set-point tracking of comparative example 2 is slightly slower, and ADRC with set-point feed-forward and conventional ADRC of comparative example 1 respond the slowest. Meanwhile, when disturbance occurs, the ADRC of the invention has equivalent disturbance rejection capability to that of the ADRC of the comparative example 2, the influence of the disturbance can be eliminated more quickly, and meanwhile, the dynamic deviation is smaller.
Fig. 5 is a control amount comparison curve when the operating condition is changed to T-30. Compared with the other three methods, the control quantity change of the ADRC of the invention is rapid and stable, not only can not cause impact on an actuating mechanism, but also can act in time, and shows good engineering applicability.
It should be noted that, in the above simulation, the second-order compensated active disturbance rejection controller based on the scheduling signal designed by the present invention does not set a feedforward function, so the curve contrast shows the effect of the compensated ADRC control based on the scheduling signal. From the simulation comparison results, it can be seen that the ADRC designed by the present invention is faster and more stable in the set point tracking without overshoot, and can also eliminate the influence of disturbance faster, and the dynamic deviation is smaller, compared to the compensation ADRC of comparative example 2, the conventional ADRC, and the ADRC with set point feed-forward of comparative example 1, showing the excellent performance of the method of the present invention.
Example 2: the controlled quantity of a main steam pressure loop of a certain coal burner unit is main steam pressure, the controlled quantity is coal feeding quantity, and a transfer function is in a high-order inertia form:
Figure BDA0003650866280000111
wherein n is 5. Load, coal feed, main steam pressure under steady-state conditions, and controlled process model under steady-state conditionsType parameter K γ2 And T γ2 See table below.
Load(s) 0 99 165 250 330
Amount of coal supplied 70 70 115 168 220
Pressure of main steam 0 9.5 13 16.5 19
K γ2 0.1357 0.1357 0.1130 0.0982 0.0864
T γ2 400 300 250 220 200
In order to illustrate the control effect of the invention, a feedforward compensation active disturbance rejection controller based on a scheduling signal is designed according to the method of the invention, and the order of the controller is taken as m-1. Taking a load instruction as a scheduling signal Q (t), referring to model information and a steady state under each working condition, and taking k f The feedforward controller is designed as follows, 0.5:
Figure BDA0003650866280000112
according to the variable working condition dynamic information of the controlled process, determining a compensation function as an inertia link with the order of p being 4, wherein the form of the inertia link is as follows:
Figure BDA0003650866280000113
wherein the time constant of the compensation function varies with the scheduling signal as follows:
Figure BDA0003650866280000114
designing the extended state observer to be of the second order with observer bandwidth omega o (t) as a function of the scheduling signal:
Figure BDA0003650866280000115
adjustable parameter of extended state observer following omega o (t) variation:
Figure BDA0003650866280000121
bandwidth omega of feedback controller c (t) and adjustable parameters vary with the scheduling signal as follows:
Figure BDA0003650866280000122
k p (t)＝ω c (t)
Figure BDA0003650866280000123
the simulation calculation period is delta T which is 0.2s, the working condition value is firstly reduced in a segmentation mode and then increased in a segmentation mode, the change rate is 0.055/s, and the set value changes along with the working condition. Meanwhile, k is respectively designed for comparing and explaining the beneficial effects of the invention f The controller order was taken to be 1 for 0, i.e. the scheduling signal based compensation ADRC without feed forward and the scheduling signal free compensation ADRC of comparative example 2. When the load changes, the controlled variable and the control variable change curves obtained by simulation are respectively shown in fig. 6 and fig. 7.
As can be seen from fig. 6: the feedforward compensation ADRC based on the scheduling signal can quickly and stably track the change of the set value no matter in a high load section, a medium load section or a low load section, and the adjusting time is obviously faster than that of the other two control methods. When k is f When the value is equal to 0, the compensation ADRC control parameter based on the dispatching signal without feedforward can change along with the load, so that the control effect is relatively consistent under different working conditions, but the response speed is obviously slower than that of the feedforward compensation active disturbance rejection controller based on the dispatching signal because the feedforward controller is not used and the adjustment is completely carried out by depending on the feedback action. The controlled quantity of the compensation ADRC without the scheduling signal of the comparative example 2 can track the change of the set value more smoothly in a high-load section, but because no signal scheduling mechanism exists, the control parameter does not change along with the working condition, so that the controlled quantity appears in a low-load sectionA significantly greater overshoot is present. By combining the comparison results, the feedforward compensation ADRC based on the scheduling signal can show more consistent and satisfactory control effect under each load when the working condition is changed in a large range, and shows excellent working condition adaptability and excellent control effect.
As can be seen from the control quantity change curve of FIG. 7, the control quantity of the ADRC of the present invention is fast and stable under various working conditions, so that the present invention has a good engineering application prospect.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. A feedforward compensation active disturbance rejection controller based on a scheduling signal is characterized by comprising a feedforward controller, a feedback controller, a compensation module and an expansion state observer;
the feedforward controller is as follows: u. of Q (t) ═ F1(q (t)), where u is Q (t) is a feedforward control quantity, Q (t) is a scheduling signal, and F1(·) is a feedforward function;
the feedback controller is as follows:
Figure FDA0003650866270000011
wherein u is C (t) is the output of the feedback controller, r (t) is a set value, z i (t) (i ═ 1,2, …, m +1) is the output of the extended state observer,
Figure FDA0003650866270000012
and b 0 (t) is an adjustable parameter and varies with the variation of the scheduling signal q (t);
the compensation module is as follows: u. of TF (t)＝F2(u C (t)，T F2 (t, p) wherein u TF (t) is the output of the compensation module, F2 (-) is the compensation function, u C (T) is the output of the feedback controller, T F2 (T) and p are adjustable parameters, T F2 (t) varies with the change in the scheduling signal q (t); output u of the compensation module TF (t) is capable of being an input to the extended state observer;
the output of the feedback controller and the output of the feedforward controller form a control law of the active disturbance rejection controller, and the control law comprises the following steps: u (t) ═ u Q (t)+u C (t), wherein u (t) is a control amount.
2. The active disturbance rejection controller according to claim 1, wherein said extended state observer is:
Figure FDA0003650866270000013
wherein y (t) is a controlled quantity, beta i (t) (i ═ 1,2, …, m +1) is a variable parameter of the extended state observer, varying as a function of the modulation signal q (t), b 0 (t) is an adjustable parameter of the feedback controller.
3. The active-disturbance-rejection controller according to claim 1, wherein a transfer function of the compensation function is:
Figure FDA0003650866270000014
wherein F2(s) is the transfer function of the compensation function, U TF (s) and U C (s) the output u of the compensation module and the feedback controller, respectively TF (t) and u C (T) pull transform, p is the transfer function order of the compensation function, T F2 (T) and p are both adjustable parameters, and T is F2 (t) varies in value as the modulation signal Q (t) varies.
4. A method for designing a feedforward compensated auto-disturbance-rejection controller based on a scheduling signal as claimed in any one of claims 1 to 3, comprising:
s1, selecting a dispatching signal Q (t) according to the variable working condition characteristics of the controlled process, and obtaining the functional relation between the dispatching signal Q (t) and the feedforward control quantity according to design calculation or field experiments;
s2, obtaining a feedforward function F1 (-) according to a function relation inverse function of the scheduling signal Q (t) and the feedforward control quantity; calculating to obtain feedforward control quantity u according to feedforward function and scheduling signal Q (t)＝F1(Q(t))；
S3, acquiring dynamic information of the variable working condition of the controlled process;
s4, designing a compensation module and a compensation function F2 (-) and obtaining the output u of the compensation module by using the variable working condition dynamic information obtained in S3 TF (t)＝F2(u C (t)，T F2 (t), p), wherein F2(·) is a compensation function, u C (T) is the output of the feedback controller, T F2 (t) and p are adjustable parameters;
s5, designing an extended state observer, wherein the output of the compensation module can be used as the input of the extended state observer to obtain the output z of the extended state observer i (t)(i＝1，2，…，m+1)；
S6, designing a feedback controller, and calculating to obtain a feedback control quantity u C (t)：
Figure FDA0003650866270000021
Wherein r (t) is a set value,
Figure FDA0003650866270000022
Figure FDA0003650866270000023
and b 0 (t) is an adjustable parameter;
s7, constructing a control law of the active disturbance rejection controller, and obtaining a control quantity of the active disturbance rejection controller through the feedforward control quantity and the feedback control quantity:
u(t)＝u Q (t)+u C (t)。
5. the design method according to claim 4, wherein the selection of the scheduling signal Q (t) satisfies the following two conditions:
(1) the variable working condition characteristics of the controlled process can be represented;
(2) has a programmable functional relationship with the amount of feedforward control.
6. The design method according to claim 4, wherein the method for acquiring the dynamic information of the variable working condition of the controlled process comprises the following steps:
dividing the variable working condition range of the controlled process into q sections according to the nonlinearity of the controlled process, obtaining the dynamic information of each section and expressing the dynamic information as follows through a controlled process transfer function:
Figure FDA0003650866270000024
where s is laplace operator, y(s) and u(s) are laplace transforms of y (t) and u (t), respectively, the subscript γ 2(γ 2 ═ 1,2, …, q) is the operating condition number, G is the operating condition number, and G is the operating condition number p，γ2 (s) is the transfer function of the controlled process under the working condition gamma 2, K γ2 System gain, T, for operating condition gamma 2 γ2 The time constant under the working condition gamma 2 is shown, and n is the order.
7. The design method of claim 4, wherein the transfer function of the compensation function is:
Figure FDA0003650866270000025
wherein F2(s) is a transfer function of the compensation function F2 (-), U TF (s) and U C (s) are each u TF (t) and u C (T) pull transformation, T F2 (t) and p are adjustable parameters.
8. Design method according to claim 4, characterized in that the output u of the compensation module TF The time domain form of (t) is:
Figure FDA0003650866270000031
where Δ T is the calculation period and k is the discrete time sequence.
9. The design method according to claim 4, wherein the extended state observer is designed to:
Figure FDA0003650866270000032
wherein y (t) is a controlled quantity, beta i (t) (i ═ 1,2, … m +1) is a tunable parameter that changes as the modulation signal q (t) changes, b 0 (t) is an adjustable parameter of the feedback controller.
10. Design method according to claim 4, characterized in that the adjustable parameters of the feedback controller
Figure FDA0003650866270000033
Comprises the following steps:
Figure FDA0003650866270000034
where m is the order of the feedback controller, ω c (T) is the feedback controller bandwidth, T γ (t) varies with the scheduling signal Q (t).
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* Cited by examiner, † Cited by third party
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CN115591378A (en) * 2022-12-12 2023-01-13 清华大学（Cn） Feedforward compensation and disturbance suppression control system and method for SCR denitration of thermal power generating unit
CN116954060A (en) * 2023-09-19 2023-10-27 中国空气动力研究与发展中心高速空气动力研究所 Control method for resisting time-varying interference of wind tunnel flow field

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115591378A (en) * 2022-12-12 2023-01-13 清华大学（Cn） Feedforward compensation and disturbance suppression control system and method for SCR denitration of thermal power generating unit
CN116954060A (en) * 2023-09-19 2023-10-27 中国空气动力研究与发展中心高速空气动力研究所 Control method for resisting time-varying interference of wind tunnel flow field
CN116954060B (en) * 2023-09-19 2023-12-05 中国空气动力研究与发展中心高速空气动力研究所 Control method for resisting time-varying interference of wind tunnel flow field

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